Luke Weiger wrote:
>
> Carrol wrote:
>
> > The universe was here before people existed. ...laws are mental.
> Patterns and regularities existed before people did. Then we came along,
> observed them, and attempted to describe
> them--and we needed mathematics to do it, just like (I'd imagine) any other
> intelligent being would've.
Only in mental space is a straight line the shortest distance between two points; and all actual lines are of course three dimensional, not one-dimensional, no matter how fine a point the drafting instrument has, or they wouldn't be visible. The theorems of plane geometry are abstractions from a world which they only approximately correspond to. Russell the mathematician was direct about this: he declared himself a Platonist in mathematics, that is, he believed in the reality of pure mathematical forms, indpendently of material embodiment. Where can a 'perfect' circle exist except in mental space (or in Plato's or Dante's empyrean)?
Carrol